Final Exam Paper - Statistics for Engineers | STAT 4705, Exams of Statistics

Download Final Exam Paper - Statistics for Engineers | STAT 4705 and more Exams Statistics in PDF only on Docsity! STAT 4705 Spring 2009 Probability & Statistics for Engineers & Scientists Virginia Tech University Score:_______ out of 100 total Final Exam Please read the following directions carefully. Failure to follow directions may result in loss of points or your exam not being graded at all. DIRECTIONS: 1. Please direct all questions concerning this exam only to the instructor. Do not collaborate with a student in the classroom during the exam. 2. For each problem involving a calculation, circle your final answer. Remember to show as much work as possible so that you get the maximum credit allowed. 3. When you finish your exam, print your name at the bottom of this cover sheet and sign the honor pledge. Submit the entire exam booklet to the instructor. 4. Do not cheat on this exam. 5. Please turn off (not on vibrate) all cellular phones and pagers before opening this booklet. If your phone or pager rings or vibrates during the examination where it disturbs your classmates (or comes to the attention of the instructor), you will receive a grade of zero. 6. Turn in your formulas sheet with the exam. I agree to take the exam under the above directions, and have completed this exam in compliance with the Virginia Tech University Honor Code. ___________________________________________ _____________________ Signature Date ___________________________________________ Print your name. 1 Problem1 (5+5+5=15p) Let X be a random variable for the number of mistakes made by data entry clerks. You know X follows a Poisson distribution with a mean of 0.8 mistakes per hour. You just gave someone applying for your data entry vacancy an hour worth of data entry material. Answer the following questions. A) What is the probability the person will make zero mistakes? B) What is the probability the person will make more than 2 mistakes? C) If a person makes 2 mistakes in the first 15 minutes you will stop the test. What is the probability that you will stop the test in the first 15 minutes? 2 Problem4 (10+5+5=20p) Let Z be the number of cars a family owns. The distribution of Z is: Z 0 1 2 3 4 f(z) .06 .26 .44 .21 .03 A) What is the mean and variance for the number of cars a family owns? B) What is the 3rd moment about the origin of the random variable Z? C) What’s the probability that a family own more than 2 cars? 5 Problem5 (10+5=15p) The shipping time for company A is normally distributed with a mean of 3.2 days and a standard deviation of 1.2 days. A competing company B advertises that their shipping time is normally distributed with an average shipping time of 3.0 days and a standard deviation of .84 days. A) Which company would you choose if you need to have the package shipped in less than two days? Justify your answer. B) You collect a sample of 36 shipped items from company A. What is the likelihood that your sample average is more than 3.6 days? 6 Problem6 (10p) A random variable, X, has a probability distribution function (pdf) given by: Find the values of a and b so that: 7 otherwise xxx xf ,10 ,0 ),1(6 )(         7500. bXaP